arXiv subjects

Bernardo Hummes Flores

Publications and source records attributed to Bernardo Hummes Flores.

3 recordsLinked to original sources

arXiv2025

Knowledge in multi-robot systems: an interplay of dynamics, computation and communication

In this paper, we provide a framework integrating distributed multi-robot systems and temporal epistemic logic. We show that continuous-discrete hybrid systems are compatible with logical models of knowledge already used in distributed computing, and demonstrate its usefulness by deriving sufficient epistemic conditions for exploration and gathering robot tasks to be solvable. We provide a separation of the physical and computational aspects of a robotic system, allowing us to decouple the problems related to each and directly use methods from control theory and distributed computing, fields that are traditionally distant in the literature. Finally, we demonstrate a novel approach for reasoning about the knowledge in multi-robot systems through a principled method of converting a switched hybrid dynamical system into a temporal-epistemic logic model, passing through an abstract state machine representation. This creates space for methods and results to be exchanged across the fields of control theory, distributed computing and temporal-epistemic logic, while reasoning about multi-robot systems.

cs.LO↗

arXiv2025

A Sheaf-Theoretic Characterization of Tasks in Distributed Systems

We introduce a sheaf-theoretic characterization of task solvability in general distributed computing models, unifying distinct approaches to message-passing models. We establish cellular sheaves as a natural mathematical framework for analyzing the global consistency requirements of local computations. Our main contribution is a task sheaf construction that explicitly relates both the distributed system and task, in which terminating solutions are precisely its global sections. We prove that a task can only be solved by a system when such sections exist in a task sheaf obtained from an execution cut, the frontier in which processes have enough information to decide. Our characterization is model-independent, working under varying synchronicity, failures and message adversaries, as long as the model produces runs composed of global states of the system. Furthermore, we show that the cohomology of the task sheaf provides a linear algebraic description of the decision space of the processes, and encodes the obstructions to find solutions. This opens way to a computational approach to protocol synthesis, which we illustrated by deriving a protocol for approximate agreement. This work bridges distributed computing and sheaf theory, providing both theoretical foundations for analyzing task solvability and tools for protocol design leveraging computational topology.

cs.DC↗

arXiv2025

A categorical and logical framework for iterated protocols

In this article, we show that the now classical protocol complex approach to distributed task solvability of Herlihy et al. can be understood in standard categorical terms. First, protocol complexes are functors, from chromatic (semi-) simplicial sets to chromatic simplicial sets, that naturally give rise to algebras. These algebras describe the next state operator for the corresponding distributed systems. This is constructed for semi-synchronous distributed systems with general patterns of communication for which we show that these functors are always Yoneda extensions of simpler functors, implying a number of interesting properties. Furthermore, for these protocol complex functors, we prove the existence of a free algebra on any initial chromatic simplicial complex, modeling iterated protocol complexes. Under this categorical formalization, protocol complexes are seen as transition systems, where states are structured as chromatic simplicial sets. We exploit the epistemic interpretation of chromatic simplicial sets and the underlying transition system (or algebra) structure to introduce a temporal-epistemic logic and its semantics on all free algebras on chromatic simplicial sets. We end up by giving hints on how to extend this framework to more general dynamic network graphs and state-dependent protocols, and give example in fault-tolerant distributed systems and mobile robotics.

cs.LO↗